Question

A pet supply chain called Paw Paw has 9 dogs and 7 cats for sale. Another supply chain called Happy feet has 14 dogs and 8 cats. Which location has a lower ratio of dogs to cat
A) Paw Paw
B) Happy Feet
C) Both are same
D) Cannot be determined

Answer 1

Hint: We use ratios to compare the values of two different things and ‘:’ sign is used to separate the two values. Ratio can be written in fraction as:
 $ a:b = \dfrac{a}{b} $
For conversion to percentage from fraction to percentage, we will first find its approximate decimal value and then multiply it with 100.

Complete step-by-step answer:
Ratio and fractions for dogs and cats for each supply chain:

	Dogs : Cats	Fraction
Paw Paw	9 : 7	$ \dfrac{9}{7} $
Happy Feet	14 : 8	$ \dfrac{{14}}{8} $

Expressing these fractions in percentage for the comparison:
 $ \dfrac{9}{7} = 1.285 $
 $ = 1.285 \times 100 $
 $ = 128.5\% $
  $ \dfrac{{14}}{8} = 1.75 $
 $ = 1.75 \times 100 $
 $ = 175\% $
 [Decimal moves to the right in case of multiplication, the number of places moved are equal to the number of zeroes].
From the comparison of fractions, we can conclude that:
Fraction for the Paw Paw is lesser as compared to the Happy feet.
This implies that the ratio of Dogs and cats of pet supply chain Paw is lower than that of Happy feet.
Therefore, the correct option is A) Paw Paw

Note: The first term of a ratio is called antecedent and the second one is called consequent. When we convert ratios into fractions, antecedent becomes numerator and the consequent becomes denominator.
For the comparison between quantities in ratios or in fractions, we generally use percentage to obtain accurate answers.